Ban Josip Jelačić Square is the main square of Zagreb and it is only 1 minute walk away. You can find public transportation in all directions at the square. Also, you have 1 minute walk to the Zagreb Cathedral on Kaptol.
You can enjoy beautiful walks around parks near center. Two most beautiful parks in center are called Zrinjevac and Ribnjak.
On European square, that is next to Ban Jelacic Square, you can find different events especially in time of holidays and other cultural events.